The objective of the geometry dash game is for the players to avoid colliding with obstacles by jumping over them.

C++ Solution

#include <bits/stdc++.h>

using namespace std;

typedef unsigned long long ULL;

const int maxn = 1e5 + 100;
int T, n;
vector<pair<int, ULL>> Edge[maxn * 5];

ULL Hash(ULL w){
    return w * 747474747 + 447474747;
}

map<ULL,int>mp;

void dfs(int u, int fa, ULL Ha){
    mp[Ha]++;
    for(int i = 0; i < Edge[u].size(); i++){
        int v = Edge[u][i].first;
        ULL w = Edge[u][i].second;
        if(v == fa) continue;
        dfs(v, u, Ha ^ w);
    }
}

int main(){
    scanf("%d", &T);
    int w, u, v;
    while(T--){
        scanf("%d", &n);
        mp.clear();
        for(int i = 0; i < n; i++) Edge[i].clear();
        for(int i = 0; i < n - 1; i++){
            scanf("%d %d %d", &u, &v, &w);
            u--; v--;
            Edge[u].push_back(make_pair(v, Hash(w)));
            Edge[v].push_back(make_pair(u, Hash(w)));
        }
        ULL ans = (1ULL * n * (n - 1)) / 2;
        dfs(0, -1, 0);
        for(map<ULL, int>::iterator it = mp.begin(); it != mp.end(); it++) {
            ans -= (it->second * (it->second - 1)) / 2;
        }
        cout << ans << endl;
    }
    return 0;
}

here is hackerrank number game on a tree solution

Description has an error: """ if the list of integers is {1,1,2,3,3,4} and Andy starts the game by removing 3... """ That is a loosing move, which players wouldn't do according to the rules.

include

// #include "testlib.h"  
using namespace std ;

#define ft first
#define sd second
#define pb push_back
#define all(x) x.begin(),x.end()

#define ll long long int
#define vi vector<int>
#define vii vector<pair<int,int> >
#define pii pair<int,int>
#define plii pair<pair<ll, int>, int>
#define piii pair<pii, int>
#define viii vector<pair<pii, int> >
#define vl vector<ll>
#define vll vector<pair<ll,ll> >
#define pll pair<ll,ll>
#define pli pair<ll,int>
#define mp make_pair
#define ms(x, v) memset(x, v, sizeof x)

#define sc1(x) scanf("%d",&x)
#define sc2(x,y) scanf("%d%d",&x,&y)
#define sc3(x,y,z) scanf("%d%d%d",&x,&y,&z)

#define scll1(x) scanf("%lld",&x)
#define scll2(x,y) scanf("%lld%lld",&x,&y)
#define scll3(x,y,z) scanf("%lld%lld%lld",&x,&y,&z)

#define pr1(x) printf("%d\n",x)
#define pr2(x,y) printf("%d %d\n",x,y)
#define pr3(x,y,z) printf("%d %d %d\n",x,y,z)

#define prll1(x) printf("%lld\n",x)
#define prll2(x,y) printf("%lld %lld\n",x,y)
#define prll3(x,y,z) printf("%lld %lld %lld\n",x,y,z)

#define pr_vec(v) for(int i=0;i<v.size();i++) cout << v[i] << " " ;

#define f_in(st) freopen(st,"r",stdin)
#define f_out(st) freopen(st,"w",stdout)

#define fr(i, a, b) for(i=a; i<=b; i++)
#define fb(i, a, b) for(i=a; i>=b; i--)
#define ASST(x, l, r) assert( x <= r && x >= l )

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

const int mod = 1e9 + 7;

int ADD(int a, int b, int m = mod) {
    int s = a;
    s += b;
    if( s >= m )
      s -= m;
    return s;
}

int MUL(int a, int b, int m = mod) {
    return (1LL * a * b % m);
}

int power(int a, int b, int m = mod) {
    int res = 1;
    while( b ) {
        if( b & 1 ) {
            res = 1LL * res * a % m;
        }
        a = 1LL * a * a % m;
        b /= 2;
    }
    return res;
}

ll nC2(ll x) {
    return ( x * ( x - 1 ) / 2 );
}

const int maxn = 5 * 1e5 + 5;

int t, n, vis[maxn], cnt;
map<int, int> M;
vii adj[ maxn ];
int prime1 = 23, prime2 = 7, base[2][maxn];
int mod1 = 1589917477;
int mod2 = 1897266401;
vii a;
void dfs(int u, int p = 0, ll cst1 = 0, ll cst2 = 0) {
    a[u-1].ft = cst1;
    a[u-1].sd = cst2;
    for( auto it: adj[u] ) {
        if( it.ft != p ) {
            if(!M.count(it.sd)) {
                M[it.sd] = cnt ++;
            }
            vis[M[it.sd]] = 1 - vis[M[it.sd]];
            cst1 += (vis[M[it.sd]] ? base[0][M[it.sd]] : -base[0][M[it.sd]]);
            cst2 += (vis[M[it.sd]] ? base[1][M[it.sd]] : -base[1][M[it.sd]]);
            if( cst1 >= mod1 ) cst1 -= mod1; if( cst1 < 0 ) cst1 += mod1;
            if( cst2 >= mod2 ) cst2 -= mod2; if( cst2 < 0 ) cst2 += mod2;
            dfs(it.ft, u, cst1, cst2);
            vis[M[it.sd]] = 1 - vis[M[it.sd]];
            cst1 += (vis[M[it.sd]] ? base[0][M[it.sd]] : -base[0][M[it.sd]]);
            cst2 += (vis[M[it.sd]] ? base[1][M[it.sd]] : -base[1][M[it.sd]]);
            if( cst1 >= mod1 ) cst1 -= mod1; if( cst1 < 0 ) cst1 += mod1;
            if( cst2 >= mod2 ) cst2 -= mod2; if( cst2 < 0 ) cst2 += mod2;
        }
    }
}

int main() {
    cin >> t;
    int sum = 0;
    while( t-- ) {
        cin >> n; sum += n;
            assert(sum <= 500000);
        int i; base[0][0] = base[1][0] = 1;
        fr(i, 1, n) {
            base[0][i] = 1LL * base[0][i-1] * prime1 % mod1;
            base[1][i] = 1LL * base[1][i-1] * prime2 % mod2;
        }
        fr(i, 1, n-1) {
            int u, v, cst; 
            cin >> u >> v >> cst;
            adj[u].pb( {v, cst} );
            adj[v].pb( {u, cst} );
        }
        cnt = 0;
        a.resize(n);
        dfs(1, 0, 0);
        assert(a.size() == n);
        sort(all(a));
        i = 0;
        ll ans = 0;
        while( i < n ) {
            pii x = a[i]; int c = 0;
            while( i < n && x == a[i] ) {
                c ++; i ++;
            }
            ans += 1LL * c * (c-1) / 2;
        }
        ans = nC2(n) - ans;
        cout << ans << "\n";
        M.clear(); a.clear();
        fr(i, 0, n) {
            adj[i].clear(); 
            vis[i] = base[0][i] = base[1][i] = 0;
        }
    }
    assert(n <= 500000);
    return 0;
}